Hisashi Murakami, Yukio Gunji

Abstract

In an intermittent random search, in which slow motion to
detect the target is discretely separated from the motion to
migrate to another feeder, the high efficiency of the Lévy
strategy is generally found, meaning that the time interval of
phase switching is chosen from the Lévy distribution. Though
the Lévy strategy is consistent with the searching behavior of
real animals, some researchers claim that the Lévy-like
distributions exhibited by animals are not necessarily produced
by a Lévy process. Here, we propose an intermittent two-phase
search model that does not include a Lévy process. In this
model, the agent is basically a correlated random walker
(CRW), but it memorizes its trajectory and counts the number
of crossovers in a trajectory. If the number exceeds a threshold,
the agent resets the memory of trajectories and makes ballistic
movement in the direction uncorrelated to the past. We also
show that this model can optimize the trade-off between macro
search (exploration) and micro search (exploitation), which is
shown by the CRW. Finally, we demonstrate that another
intermittent search model that uses an ambiguous rule to switch
the two phases can show a Lévy-like distribution of time
intervals.